Least action principle of crystal formation of dense packing type & the proof of keplers conject...


Least action principle of crystal formation of dense packing type & the proof of keplers conject...


Wu Yi Hsiang, "Least Action Principle of Crystal Formation of Dense Packing Type & the Proof of Keplers Conjecture"
2002 | pages: 425 | ISBN: 9810246706 | DJVU | 2,1 mb



The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal "known density" of B/+18. In 1611, Johannes Kepler had already "conjectured" that B/+18 should be the optimal "density" of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Keplers conjecture that B/+18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques and in the tradition of classical geometry.


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